For some people they are pets, for some livestock. For many somewhere in between. I like the way someone else expressed it recently. Look at the flock as the pet and the individual chickens as replaceable parts in the flock.
I don’t know why you are thinking about removing them but you obviously feel about it a lot differently than I do. I know from the start that mine will be eaten, it’s a big part of why I have chickens to start with. I don’t enjoy the killing part but it’s a necessary part of me keeping chickens so I do it.
I don’t know your motivation, but if you had a dog that was broken down and in great misery would you take it to the vet to be put down or just let it continue to suffer? I doubt your six year old chickens are in misery but can you draw a parallel?
Some people keep them until they die of old age. There is nothing wrong with that if that is your choice. It’s not my choice but I will not criticize you for choosing that. Don’t beat yourself up about it if that is your choice.